Battle of Britain

The name given to the air battle over British land which took place in the summer of 1940.Hitler (and his axis allies) had already managed to invade the rest of Europe. Hitler's next move was to invade Winston Churchill's Britain (thus removing one front from the war) this planned invasion was called Operation Sea Lion but Hitler knew that for it to be a success he would need control of the skies over the channel and the British coast.

The Luftwaffe was considerably bigger than the RAF but the RAF had some advantages:

Britain was very industrialised and perfectly capable of churning out quantities of aircraft, Its only problem was a shortage of pilots.

With the Battle being conducted over British land many British pilots who were shot down could quickly be placed back in an aircraft, The British pilots were fighting over known territory and they had longer fighting time as the Nazi planes had to use most of their fuel to get to and from friendly territory

Radar. The British had just implemented a comprehensive radar system so they knew where, when and how many aircraft were invading, this allowed even far off squadrons to be in place before the Nazis reached British territory.

At first the Luftwaffe aimed its attacks directly at the RAF, attacking airbases and radar installations alike with a ferocity so great that it is said that some ground staff refused to get out of their air raid shelters for days afterwards. This period caused great damage to the RAF and could have very easily destroyed it if two major errors hadn't been made.
The first error was Aldertag (eagle day) which was supposed to happen on the 13 August. The plan was to do one extremely large co-ordinated strike involving many fighter and bomber squadrons. The day turned out to be foggy (or some bad weather like that) so the Luftwaffe high command ordered a postponement. Not all squadrons heard the message so some bombers set out for Britain unescorted. Realising this, the Nazis sent out the rest of the squadrons anyway. As a result the Nazis suffered heavy losses.
The second mistake was a curious decision to change tactics. All of a sudden (7 september) the attention turned from the RAF to major cities (possibly in an attempt to draw out the RAF to fight or maybe as a reaction to an Allied bombing of Berlin), especially London, this was called the Blitzkreig. This gave the RAF time to rebuild itself and carry on the fight.

Hitler officially gave up on Operation Sea Lion on 21 September and the Battle of Britain was won but it wasn't until May 1941 that the Blitzkreig ended.